Now I am not sure why the judge is requesting this, not what Andrews team can do to counter it, if at all. Presumably they could launch a motion in the UK requesting that the UK courts tell the US courts to go fuck themselves ? However is it the UK courts place to question the basis of the request ? As long as it is correctly relayed through the system(s), it should be honoured.
The judge is requesting it because Giuffre's lawyers have asked him to do so and he has agreed to their request. Similarly, he has relayed a request from Andrew's lawyers to the Australian authorities.
I am not an expert in this process, but my understanding is that it is highly unlikely Andrew could get this thrown out, although he may be able to challenge conditions or terms of the order being made.
Which then leads to what options Olney has at this point. Indeed what jurisdiction the evidence would be given under. Since UK law has no concept of the fifth amendment.
We do have the same concept as the fifth amendment - a witness can refuse to answer any question if it would be self-incriminating. However, to answer the question, Olney and the other requested witness would be compelled to testify (as can happen in UK cases). When giving their evidence, they would be entitled to claim the any privilege from answering questions that is available to them under either UK or US law.